DR. BADAM SINGH KUSHVAH

The stability and chaos play an important role to understand the nature of dynamical system. We apply conditions of linear stability to the particular dynamical system which is a modified restricted three body problem. The dynamical behaviour of nearby trajectories is being estimated by Lyapunov Characteristic Exponents(LCEs). It is found that the trajectories of the Lagrangian point equilibrium point moves along the epicycloid path, and spirally departs from the vicinity of the point. The LCEs remain positive for all the cases and depend on the initial deviation vector as well as renormalization time step. Finally, we find that the trajectories are chaotic in nature and the equilibrium point is asymptotically stable.